This invention relates generally to medical imaging systems, and more particularly, to image reconstruction using Positron Emission Tomography (PET).
PET generates images that represent the distribution of positron-emitting nuclides within the body of a patient. When a positron interacts with an electron by annihilation, the entire mass of a positron-electron pair is converted into two 511-keV photons. The photons are emitted in opposite directions along a line of response. The annihilation photons are detected by detectors that are placed on both sides of the line of response, in a configuration such as a detector ring. When these photons arrive and are detected at the detector elements at the same time, this is referred to as coincidence. An image is then generated based on the acquired image data that includes the annihilation photon detection information.
In PET scanners, the image quality depends on image statistics. The image statistics may be improved by acquiring the image data for longer durations. However, the total time of acquiring the image data is limited by the decay of radioactive isotope and by the inability of the patients to not move for extended durations.
Image quality may be improved by including time-of-flight (TOF) information for the image data. The TOF is the time taken by an annihilation photon to travel from the origin of annihilation to the detector along the line of response. TOF PET also uses the timing difference at which the photons are detected by the detector elements for the reconstruction of an image. If the distance between two detector elements P and Q is 2A and annihilation of a positron-electron pair occurs at the midpoint of the line joining the two detector elements, the time taken by each photon to reach the detector element is A/c, where c is the speed of light. In this case, the timing difference is zero. If the annihilation occurs at a distance x towards detector element P, the time taken by the photons to reach detector elements P and Q is (A−x)/c and (A+x)/c respectively. In this case, the timing difference is 2x/c, which may also be expressed as x/(c/2). The timing difference is used to reconstruct an image along the line joining two detector elements in TOF PET systems.
In order to maintain high resolution of images in the reconstruction process in TOF PET systems, it is typically important to measure the timing difference accurately. A systematic error, or bias, in the estimation of the timing difference between photon detection in the two detectors will translate into a shift of the estimated source of photon annihilation along the line joining two detector elements because calibration errors result in a timing bias. If the timing bias is 0.1 nanoseconds (ns), the reconstruction process shifts the data along the line between the detector elements by 1.5 cm. Such shifts make it difficult to achieve resolution of the order of 0.5 cm or better. Thus, high resolution image reconstruction of smaller objects (e.g., smaller anatomical structures) is difficult, if not impossible.
In known TOF PET systems, the timing difference is measured by determining the overlap of analog pulses representing the arrival time of the photons at the detector elements. The analog pulses are communicated through an AND gate to determine coincidence. Each individual detector element has its own set of electronics that is adjusted to remove the timing biases. However, the timing performance of each channel may drift or shift over time, for example, as the electronics used becomes warmer during longer operating periods. Therefore, it is difficult to tune or calibrate these systems to maintain the desired level of accuracy in reconstruction.
In other known TOF PET systems, the photon arrival time is digitized and coincidence is determined by comparing the digital time stamps for each measured photon. The system is tuned or calibrated by introducing a variable amount of delay in the signal before it is digitized in each detector element. However, a system with a large number of detector elements will, for reasons of economy of manufacture, use a common set of electronics to process a group of detector elements. It is commonly not known which detector within the group has received a photon, and therefore which value of the delay should be applied to the signal before the signal is digitized and processed. Therefore, differences in the timing bias among the detectors in a group cannot be individually corrected by adjusting the electronics as described above, and, if these differences are significant, there will be a loss of accuracy in the reconstructed image.
Another known method of tuning a TOF PET system is to introduce a delay after the signal is digitized by changing the digital time stamp. In this case, the timing signal from each individual detector element can only be adjusted in multiples of the LSB, even though the system may have the capability to determine that the timing is some fraction of the LSB. The adjustment can reduce the timing bias to only ±½ LSB. Because this occurs for each of the two photons in the coincidence pair, the timing bias for the coincidence pair may be as large as ±1 LSB. For example, if the LSB is 500 picoseconds (ps), it corresponds to a location error of up to ±3.75 cm along the coincidence line of response. This makes it difficult, if not impossible, to achieve sub-centimeter resolution in a TOF PET system.